1. PHASE TYPE QUEUEING MODEL OF SERVER VACATION, REPAIR AND DEGRADING SERVICE WITH BREAKDOWN, STARTING FAILURE AND CLOSE-DOWN
- Author
-
G. Ayyappan and S. Meena
- Subjects
Markovian Arrival Process ,Breakdown ,Close-down ,Starting failure ,Phase type Distribution ,Degrading Service ,Server Vacation ,Matrix-analytic method ,Repair - Abstract
We consider a single server phase type queueing model with server vacation, repair, breakdown, degrading service, starting failure and closedown. When the arrival rate of the customer follows the Markovian Arrival Process (MAP) and the service rate of the server follows the phase-type distribution. If no one is in the system when the server is back from the vacation, then the server will wait until the customer arrives. If the customer arrives at the moment with no starting failure, then he provides service, otherwise the server immediately goes to the repair process. Here, the service rate declining until degradation fixed. After completion of K services the degradation is addressed. During the period of service, the server may get a breakdown at any moment, and then the server immediately goes for a repair process. After completing the service, he switches to the close-down process, and then he goes on vacation. Using the Matrix-Analytic method, The stationary probability vector representing the total number of customers in the system is examined. The analysis of the busy period, the mean waiting time, and cost analysis are discussed. A few significant performance measures are attained. Finally, some numerical examples are given.
- Published
- 2023
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